- #1
mothership
- 1
- 0
<br />
\begin{equation*}<br />
\begin{split}<br />
\int_{1}^{9} \frac{3x-2}{\sqrt{x}}dx &= \int_{1}^{9}\frac{3x}{x^{\frac{1}{2}}}dx - \int_{1}^{9}\frac{2}{x^{\frac{1}{2}}}dx \\ \\<br />
&= 3\int_{1}^{9}x^{\frac{1}{2}}dx - 2\int_{1}^{9}x^{\frac{-1}{2}}dx \\ \\<br />
&= 3 \left[ \frac{2}{3}(x^{\frac{3}{2}}) \right]_{1}^{9} - 2 \left[ 2x^{\frac{1}{2}} \right]_{1}^{9} \\ \\<br />
&= 2 \left[9^{\frac{3}{2}} - 1 \right] - 4 \left[ 9^{\frac{1}{2}} - 1 \right] \\ \\<br />
&= 2 \left[27 - 1 \right] - 4 \left[ 3 - 1 \right] \\ \\<br />
&= 2*26 - 4*2 \\ \\<br />
&= 44 \\<br />
\end{split}<br />
\end{equation*}<br />